I've applied to several programs at several different graduate schools, and if shortlisted for interview, I expect to receive invitations by the end of January and most of them hold their visit and interview event on just two weekends in Feb. I already received an invitation, but the date will have a conflict if I receive an invitation from a few schools that I actually prefer over this one. I expect to hear from those school over the next week, but I don't know if it is ok to keep them waiting for my response to interview invitation. Is this ok to respond for making arrangements a few days after receiving the invitation?
Note 1 - The event is a 2-day event, so it is not just a short interview with me, so I am worried they might not be able to rearrange a different date only for me.
Note 2 - I have already read this and this, but my question is different! It is about whether I should keep the first one waiting to avoid a potential conflict with the interview for a preferred program.